Brian Cox – the Hollywood actor, not the prof – is standing on the top floor of BBC TV Centre. “This place holds so many memories,” he says, gazing wistfully down into the circular courtyard at the building’s heart. Here, in 1968, he made The Year of the Sex Olympics, “another sensational sci-fi in its day” and, in 1974, The Changeling with Helen Mirren. “We kissed.” He was also a habitué of the bar of the BBC Club: “I remember being carried out of there at two in the morning on many occasions.”

Oddly, the bar is where, in 1965, Cox met the man he’s playing today, Sydney Newman, the former head of drama and creator of Doctor Who. “He was different from all the other people around. Everybody was still very much in BBC suits and waistcoats, pipe-smoking. Sydney was brash, mogul-like and had this Canadian-Jewish accent. He’d say, ‘How are you, kid? Are you OK? Enjoying yourself? That’s good, GOOD.’ It was not what you were expecting.”

Cox is a formidable presence, too (he was first to play the role of Hannibal Lecter!) and I’m lucky to catch him because he’s required in every scene. But he’s happy to chat between takes, even after grazing his knuckles on a stiff set door. He’s been filming a scene in Newman’s seventh-floor office where he muses on what kind of sci-fi show (“Fun, FUN. You heard of fun?”) can plug the gap in the Saturday schedule between Grandstand and Juke Box Jury. That show would be Doctor Who.

Everyone is keenly aware that An Adventure in Space and Time will be the last drama made at TV Centre before it shuts down, and they’re not using the studios but actual offices and corridors, redressed to their 1960s heyday. Producer Matt Strevens says, “It’s bittersweet because so much of it is empty now.” But he feels very lucky: “So often in period dramas, you can never go to the right place, but we’ll have spent seven days filming here out of a 22-day shoot.”

I leave Strevens (and director Terry McDonough) poring over that week’s Radio Times, which has published the first photos from An Adventure, and go down two floors to meet the actress on its cover. Call the Midwife star Jessica Raine has landed the part of Verity Lambert, Doctor Who’s original producer, who died in 2007.

Their paths never crossed, but Raine has watched lots of interviews with Lambert. “When you first hear what she did, which was become the first female drama producer at the BBC, you think, ‘Wow, she must have been a real ball-buster.’ But what I got from the old footage more than anything is that she was a warm, composed and compassionate woman.”

Raine is loving the 1960s fashions, “gorgeous shift dresses, simple classic designs. Verity was a classy woman. We’re introduced to her at her house at a party. She held fantastic soirées. She was really into art and would get all these artists’ works and hang them around her house. I felt very cool dancing with my cigarette. That’s the kind of woman I want to be.”

Next, I bump into Mark Gatiss who gives me a tour of the fifth floor, which is decked out as production offices with retro typewriters, draftsmen’s easels, pencil sharpeners… Not a PC in sight. Given our similar ages (late 40s), he susses, “We’re both Jon Pertwee boys!” Much as we were fans of the third Doctor, we both adore this earlier era, too.

The project is “a labour of love” for Gatiss. “I first started talking about doing it 12 or 13 years ago.” So far they’ve filmed “all the ‘civvies’ [scenes in everyday clothes], but we’ve done one little bit with David Bradley dressed as the Doctor, which made my heart flip.”

What’s he most looking forward to? “Seeing the original Tardis and everybody dressed up, and the junkyard from the first episode. And the planet Vortis. It’s so exciting!”

INVASION OF THE DALEKS 17 February 2013

There’s not much that would entice me out of bed at 6am on a chilly Sunday morning — but Daleks on Westminster Bridge… Oh yes! mark Gatiss and the Adventure crew are re-creating one of the classic images from Doctor Who — Daleks gliding across the Thames with Big Ben as a backdrop. And, just as in 1964, it has to be shot at dawn to avoid passers-by or disruption to traffic.

Producer Matt Strevens explains: “The plan is we have a camera positioned on top of County Hall and we also have a wide shot of the Houses of parliament and the four Daleks travelling across. And there’s just a short moment with the [1960s] director Richard Martin and a little team shooting it.” Martin, seen berating the Dalek operators, is played by Ian Hallard, Gatiss’s real-life civil partner.

By 10am the shots are in the can and the Daleks packed away..

SPOTTED – PETER CAPALDI 25 February 2013

I am sitting on a chair inside the original Tardis control room at Wimbledon Studios, nursing a blister after touching a hot bulb on the central console. Gatiss tells me everyone’s got a similar injury and weirdly I’ll treasure mine. I’m in fan-boy heaven. As I said, I’m inside the original Tardis, a set re-created in painstaking detail; it’s even painted a sickly green, which made it look whiter than white on 1960s monochrome TVs.

But so much for the past. Also standing in the studio shadows is one Peter Capaldi. He’s here as Gatiss’s friend and a lifelong fan, thrilled just to observe. I sidle up and we chat briefly about the theme of An Adventure: a star getting then letting go of a defining role, as he did with Malcolm Tucker in The Thick of It. February is a long time ago, but I can’t help wondering if Capaldi knew then that he’d soon become the 12th Doctor…

On the other side of the studio, the cast is running through a scene from Marco Polo, a historical Doctor Who story from 1964, which finds David Bradley as William Hartnell in a grumpy mood. Later, he’s on better form, dressed in the regalia of an officer during the French Revolution, greeting his grandchild between takes.

Today is special because Hartnell’s real-life granddaughter, Jessica Carney, is on set. She tells me, “It’s thrilling and poignant watching my grandparents. Quite delightful.” Also, she’s brought along the ring and Astrakhan fur hat that Hartnell wore as the Doctor, which she insists that Mark Gatiss momentarily dons.

Here’s a photo opportunity, but I’ve had to put away my camera. The BBC publicist has vetoed any photos, although Gatiss takes a few of me in the Tardis on his iPhone. (Friend for life!) He leads me backstage where monsters are being made. Four Daleks line the corridor. He’s thinking of buying one. He shows me a ghoulish cloth mask, which I fail to recognise as one of the original Cybermen, and the heads of three Menoptra (giant butterflies from 1965’s The Web Planet). A designer is struggling to construct their wings. No giant-ant Zarbi, though, says Gatiss: “We can’t afford them.”

Sacha Dhawan, the former History Boys actor, has just filmed his last scene as director Waris Hussein – one of the few still alive from those early days. Dhawan has been able to study him closely. “Waris probably doesn’t know this but when I spent a lot of time with him, it was also to see his mannerisms. I took certain things he might only spot when he watches it. I recorded our conversations and listened to them endlessly. I want to do him justice. It’s his story as well.”

Although I speak with David Bradley in the snack bar, he’s in every scene today so our interview takes place some time later. Gatiss offered him the role of Hartnell last year, tapping him on the shoulder while they were watching the Queen’s Diamond Jubilee flotilla from a rainy balcony at the National Theatre.

“I was so thrilled. Absolutely blown over.” Bradley immediately studied the early episodes, as well as key Hartnell films such as Brighton Rock and This Sporting Life. “He was one of those brilliant, iconic British actors. I’m young enough to remember him as the Doctor. That was before I even thought of becoming an actor, so if you’d said to me one day I’ll be playing that man, it would have been unthinkable.”

He’s delighted to be working with Brian Cox again. In the early 1990s, they toured the world in King Lear, and Bradley won the Olivier award for playing the Fool, but he reckons An Adventure in Space and Time is the highlight of his career so far. “It’s one of those really special jobs, playing someone who I admired as an actor, and I just hope his family are pleased with the portrait.”